A plane electromagnetic wave travelling in free space is represented by E(x,t)=E0sin(kx−ωt).
Answer the following questions.
(i) Define the phase of a wave. For the above expression, write the mathematical term that represents the phase at position x and time t.
(ii) At a fixed position x, explain qualitatively how the phase changes with time and hence state the sense in which the wave propagates.
(iii) For two points P and Q separated by a distance Δx along the x-axis, derive an expression for their phase difference in terms of Δx and wavelength λ. Hence, determine the separation required for a phase difference of π.